Eden Hazard made the breakthrough for Chelsea on 25 minutes when he raced on to a precise through-ball from Mateo Kovacic to finish low past Alisson.
Kepa Arrizabalaga saved well from Sadio Mane, before David Luiz had to clear a Roberto Firmino header off the line as Liverpool pressed for an equaliser.
It came in the final minute of normal time from Sturridge, just three minutes after coming on, as the former Chelsea forward curled a fantastic 30-yard strike into the top corner.
An end to their winning start means Liverpool drop to second, with 19 points, behind Manchester City on goal difference.
Chelsea are third on 17 points.
Chelsea: 7 Oct v Southampton (A)
Liverpool: 7 Oct v Man City (H)